Tearing Mode Stability Research Articles

Initial results from neoclassical tearing mode stabilization experiment in KSTAR high normalized beta plasmas

Abstract Active stabilization of neoclassical tearing modes (NTMs) is critical for high beta plasma operation in the KSTAR tokamak. In recent device operation, an experiment was conducted to develop a m/n = 2/1 NTM stabilization in high normalized beta (β N) plasmas having β N > 3 by using electron cyclotron current drive (ECCD). The experiment is designed to first demonstrate the direct mode stabilization effect of the device EC system by varying the ECCD deposition location around the mode rational surface to prepare for future NTM stabilization in KSTAR using feedback schemes. In the experiment, the toroidal magnetic field strength, B T, is reduced to 1.5–1.6 T to create a highly localized ECCD profile on a large island width expected to produce a high stabilization effect. To align the ECCD with the mode, B T is varied between discharges by keeping the EC wave injection angles fixed to move the current deposition location across the q = 2 mode rational surface in ∼1 cm steps along the plasma midplane. The result shows a prompt reduction of the mode amplitude by ∼60% with a partial recovery of the loss of stored energy when the ECCD with 0.7 MW power is applied promptly after the mode onset at B T = 1.54 T. This abrupt reduction of the mode amplitude is significantly weaker or disappears in other discharges having slightly different B T in which the ECCD is deposited a few centimeters away. This result indicates a direct interaction between the driven EC current and the radially localized island structure first observed in the device. The EC ray-tracing analysis using the TORAY code shows that the applied EC-driven current aligns with the mode rational surface when the mode amplitude is observed to decrease. The stability of the observed 2/1 NTM is examined by constructing the modified Rutherford equation (MRE). The calculated EC power requirement for complete mode stabilization by assuming perfect alignment of ECCD on the mode is 0.8–1.7 MW by considering the uncertainties in the equation. This MRE-computed mode stability agrees with the experiment. The result projects that the present KSTAR EC system can stabilize the 2/1 NTM disrupting high β N plasmas, and provides the requirement of the mode-ECCD alignment for complete mode stabilization in future experiments in which an accurate alignment is planned to be made by feedback schemes being developed.

Influence of plasma density gradient on the tearing mode with the poloidal shear flow

The influence of the plasma density gradient on the m/n = 2/1 and m/n = 4/1 (m is the poloidal mode number and n is the toroidal mode number) tearing mode instability with poloidal flow and flow shear is investigated. Using the analytical solution that we obtained in a previous work and mainly focused on the factors of plasma density and poloidal shear flow, we found that the plasma density has a stabilizing effect on the classical tearing mode, and the poloidal equilibrium flow can intensify this beneficial effect. The density gradient was detrimental to the stability of the tearing mode. The effects of both density and density gradient are slight, but the effect of poloidal flow on the plasma density is significant. Considering that the plasma density changes with the poloidal flow, the values of the tearing mode stability index ∆′ clearly change. Our investigation also found that compared with the negative flow shear, the positive flow shear is beneficial to the stability of the tearing mode, and a larger poloidal flow shear has a better stabilizing effect on the classical tearing mode.

Calculation of tearing mode stability in an inverse aspect-ratio expanded tokamak plasma equilibrium

The tearing mode stability of an inverse aspect-ratio expanded tokamak plasma equilibrium of general shape is investigated using asymptotic matching techniques. Particular emphasis is placed on the conservation of toroidal electromagnetic angular momentum. The TJ code, which is a specific implementation of the results of the investigation, is described.

Suppression of the m/n = 2/1 tearing mode by electron cyclotron resonance heating on J-TEXT

Stabilization of tearing modes and neoclassical tearing modes is of great importance for tokamak operation. Electron cyclotron waves (ECWs) have been extensively used to stabilize the tearing modes with the virtue of highly localized power deposition. Complete suppression of the m/n = 2/1 tearing mode (TM) by electron cyclotron resonance heating (ECRH) has been achieved successfully on the J-TEXT tokamak. The effects of ECW deposition location and power amplitude on the 2/1 TM suppression have been investigated. It is found that the suppression is more effective when the ECW power is deposited closer to the rational surface. As the ECW power increases to approximately 230 kW, the 2/1 TM can be completely suppressed. The island rotation frequency is increased when the island width is reduced. The experimental results show that the local heating inside the magnetic island and the resulting temperature perturbation increase at the O-point of the island play dominant roles in TM suppression. As the ECW power increases, the 2/1 island is suppressed to smaller island width, and the flow shear also plays a stabilizing effect on small magnetic islands. With the stabilizing contribution of heating and flow shear, the 2/1 TM can be completely suppressed.

Neoclassical tearing mode stabilization by electron cyclotron current drive in EAST tokamak experiments

The stabilization of the m/n= 2/1 neoclassical tearing mode (NTM) by electron cyclotron current drive (ECCD) has been carried out in EAST H-mode discharges, where m/n is the poloidal/toroidal mode number. The experimental results are reported for the first time in this paper. To facilitate the experimental study, the magnetic island (NTM) is generated by a sufficiently large amplitude of the externally applied resonant magnetic perturbation (RMP). After switching off the RMP, the NTM exists due to the bootstrap current perturbation, with the magnetic island width being about 5 cm for the local equilibrium bootstrap current fraction being larger than 10%. By applying the localized ECCD later, the NTM is fully suppressed if the radial misalignment between the magnetic island and the ECCD location is sufficiently small. The stabilizing effect depends on both the radial misalignment and the applied electron cyclotron wave power. More importantly, it is found that the NTM can be avoided when applying ECCD earlier during the ramp-up phase of the RMP amplitude, if ECCD is localized around the O-point of the magnetic island, indicating an efficient way for avoiding locked modes that can lead to the major disruptions of tokamak plasmas.

Effect of anisotropic thermal transport on tearing mode stability in negative versus positive triangularity plasmas

The combined effects of anisotropic thermal transport and the plasma shaping, including negative triangularity, on the n = 1 (n is the toroidal mode number) tearing mode (TM) stability are numerically investigated utilizing the MARS-F code [Liu et al., Phys. Plasmas 7, 3681–3690 (2000)]. While varying the plasma boundary triangularity, the TM stability is found to be dictated by the competing effects of the Shafranov shift induced stabilization and the bad-curvature induced destabilization. The negative triangularity shape increases the Shafranov shift (stabilizing) in the plasma core but also enlarges bad-curvature regions (destabilizing) near the plasma edge, with the net effect being largely destabilizing for the TM as compared to the positive triangularity counter-part. Large negative triangularity however can also lead to more stabilization for the plasma core-localized TM. Anisotropic thermal transport reduces the stabilizing effect on the TM associated with the favorable averaged curvature, resulting in more unstable core-localized TMs in both negative and positive triangularity plasmas. But the opposite effect can also take place for the edge-localized TM in finite-pressure plasmas with negative triangularity.

Global linear and nonlinear gyrokinetic simulations of tearing modes

To better understand multi-scale interactions between global tearing modes and microturbulence in the Madison Symmetric Torus (MST) reversed-field pinch (RFP), the global gyrokinetic code Gene is modified to describe global tearing mode instability via a shifted Maxwellian (SM) distribution consistent with experimental equilibria. The implementation of the SM is tested and benchmarked by comparisons with different codes and models. Good agreement is obtained in code-code and code-theory comparisons. Linear stability of tearing modes of a non-reversed MST discharge is studied. A collisionality scan is performed to the lowest order unstable modes (n = 5, n = 6) and shown to behave consistently with theoretical scaling. The nonlinear evolution is simulated, and saturation is found to arise from mode coupling and transfer of energy from the most unstable tearing mode to small-scale stable modes mediated by the m = 2 tearing mode. The work described herein lays the foundation for nonlinear simulation and analysis of the interaction of tearing modes and gyroradius-scale instabilities in RFP plasmas.

Analysis of neoclassical tearing mode stabilization experiment by electron cyclotron injection in KSTAR

We report the neoclassical tearing mode (NTM) stabilization experimental results by injection of the electron cyclotron (EC) beam in KSTAR, and its analysis with integrated modelling. In the KSTAR experiment, NTM was intentionally induced and the EC beam was injected by the plasma control system (PCS) to stabilize it. Here, the EC angle was controlled based on the minimum seeking algorithm for the island growth rate. Although the EC angle was not changed significantly, the island width significantly decreased towards the end of the experiment followed by the recovery of plasma performance. To assess the NTM stabilization experiment from a stability perspective, we performed integrated modelling with TRIASSIC utilizing the reconstructed equilibrium with magnetic diagnostics and motional stark effect diagnostics. As a result, we observed that the NTM is stabilized by EC.

Self-consistent study of tearing mode with finite current gradient in the resistive-inertial and viscous-resistive regimes

Via the two-field reduced magneto-hydrodynamics model, a self-consistent theory of tearing mode evolution is developed to study the stability of tearing mode in the resistive-inertial and viscous-resistive regimes. Based on the series expansion method, we obtain a closed system for tearing mode evolution with the finite current gradient (FCG) effect. Solving the closed system with correlated approximations, the dispersion relation of tearing mode with FCG in the resistive-inertial and resistive-viscous regimes is derived and discussed. Self-consistent calculations adopted in this work show that assumptions used in previous studies are not always appropriate. Furthermore, deviation from those assumptions provides a non-negligible effect to the stability of tearing mode.

Resistive instabilities in toroidal anisotropic plasmas

Resistive singular layer equations are developed by applying the magnetohydrodynamic (MHD) model to toroidal anisotropic plasmas. This work extends the previous ideal MHD theory [Shi et al. Phys. Plasmas 23, 082121 (2016)] to the resistive case. These layer equations can be used to investigate resistive localized MHD instabilities, such as tearing instability and resistive interchange instability. Compared to existing resistive theory [Johnson and Hastie, Phys. Fluids 31, 1609 (1988)], our model includes plasma compressibility, allowing for a study of the coupling between parallel motion to perpendicular one, which is known as the apparent mass effect. In addition, these obtained equations are valid for low n modes, where n is the toroidal mode number. The dispersion relation is derived in a reduced model. We find that the anisotropic pressure effect (when p⊥ > p‖) not only increases the stable threshold of the resistive interchange mode but also raises the critical value Δc of the tearing mode stability index Δ′, which represents the logarithmic jump of the radial magnetic field perturbation across the rational surface. This discovery holds significant practical implications for mitigating neoclassical tearing modes in high confinement plasmas, particularly those characterized by a low aspect ratio (such as spherical tokamaks) or low magnetic shear (as designed in ITER hybrid scenarios). However, it enhances the growth rate of the tearing mode in a low growth rate region, where p‖ and p⊥ denote the pressure components parallel and perpendicular to the magnetic fields, respectively.

Empirical probability and machine learning analysis of m, n = 2, 1 tearing mode onset parameter dependence in DIII-D H-mode scenarios

m, n = 2, 1 tearing mode onset empirical probability and machine learning analyses of a multiscenario DIII-D database of over 14 000 H-mode discharges show that the normalized plasma beta, the rotation profile, and the magnetic equilibrium shape have the strongest impact on the 2,1 tearing mode stability, in qualitative agreement with neoclassical tearing modes (m and n are the poloidal and toroidal mode numbers, respectively). In addition, 2,1 tearing modes are most likely to destabilize when n > 1 tearing modes are already present in the core plasma. The covariance matrix of tearing sensitive plasma parameters takes a nearly block-diagonal form, with the blocks incorporating thermodynamic, current and safety factor profile, separatrix shape, and plasma flow parameters, respectively. This suggests a number of paths to improved stability at fixed pressure and edge safety factor primarily by preserving a minimum of 1 kHz differential rotation, increasing the minimum safety factor above unity, using upper single null magnetic configuration, and reducing the core impurity radiation. In addition, lower triangularity, lower elongation, and lower pedestal pressure may also help to improve stability. The electron and ion temperature, collisionality, resistivity, internal inductance, and the parallel current gradient appear to only weakly correlate with the 2,1 tearing mode onsets in this database.

Effect of negative triangularity on tearing mode stability in tokamak plasmas

The influence of negative triangularity (NT) of the plasma shape on the n = 1 (n is the toroidal mode number) tearing mode (TM) stability has been numerically investigated, with results compared to that of the positive triangularity (PT) counterpart. By matching the safety factor profile for a series of toroidal equilibria, several important plasma parameters, including the triangularity, the plasma equilibrium pressure, the plasma resistivity as well as the toroidal rotation, have been varied. The TM localized near the plasma edge is found to be more unstable in the NT plasmas as compared to the PT counterpart. The fundamental reason for this difference is the lack of favorable average curvature stabilization in NT configurations. Direct comparison of the Mercier index corroborates this conclusion. For the core-localized mode, where the difference in the local triangularity between NT and PT becomes small and the curvature stabilization is significantly reduced, larger Shafranov shift in the plasma core associated with the NT configuration results in more stable TM. The plasma toroidal flow generally stabilizes the TM in plasmas with both NTs and PTs. The flow stabilization is however weaker in the case of negative triangularity with finite plasma pressure.

Validation of the current and pressure coupling schemes with nonlinear simulations of TAE and analysis on the linear stability of tearing mode in the presence of energetic particles

Both current and pressure coupling schemes have been adopted in the hybrid kinetic–magnetohydrodynamic code CLT-K recently. Numerical equivalences between these two coupling schemes are strictly verified under different approximations. First, when considering only the perturbed distribution function of energetic particles (EPs), the equivalence can be proved analytically. Second, when both the variations of the magnetic field and the EP distribution function are included, the current and pressure coupling schemes numerically produce the same result in the nonlinear simulations. On this basis, the influences of co-/counter-passing and trapped EPs on the linear stabilities of the m/n = 2/1 tearing mode (TM) have been investigated (where m and n represent the poloidal and toroidal mode numbers, respectively). The results of scanning of EPs show that the co-passing and trapped EPs are found to stabilize the TM, while the counter-passing EPs tend to destabilize the TM. The behind (de)stabilization mechanisms of the TM by EPs are carefully analyzed. Furthermore, after exceeding critical EP betas, the same branch of the high-frequency mode is excited by co-/counter-passing and trapped EPs, which is identified as the m/n = 2/1 energetic particle mode.

High power mm-wave loss measurements of ITER ex-vessel waveguide components at the FALCON test facility at the Swiss Plasma Center

Many future fusion devices will rely heavily, if not solely, on electron cyclotron (EC) heating subsystems to provide bulk heating, instability control (neoclassical tearing mode (NTM) stabilization), and thermal instability control. Efficient use of the installed heating power (gyrotrons) requires low-loss transmission of the power over 100s of meters since the mm-wave sources need to be installed where the stray magnetic field has a small amplitude. Transmission lines are used to propagate the mm-wave power over this long distance. Quasi-optical techniques (mirrors) are used at W7X and are planned for DTT, for example. Guided components are installed at DIII-D, TCV and elsewhere and are planned at JT60SA and ITER. High power test facilities exist to evaluate the power transmission of assemblies of guided components (transmission lines). The European test facility FALCON was setup by Switzerland and Fusion for Energy (F4E) in Lausanne Switzerland at the Swiss Plasma Center (SPC) in the Ecole Polytechnique Fédérale de Lausanne (EPFL). Operations are funded through a framework contract with F4E. SPC operates the facility. Two ITER-class 170GHz gyrotrons are housed within the facility and used to evaluate the thermal behaviour of components provided by various ITER partners. Loss measurements are presented for miter bends and waveguides of several materials at two different diameters. The results are used to model the expected losses in the ITER ex-vessel waveguides (EW) of all five EC launchers.

Investigation of electron cyclotron current drive efficiency on the J-TEXT tokamak

Electron cyclotron current drive (ECCD) efficiency research is of great importance for the neoclassical tearing mode (NTM) stabilization. Improving ECCD efficiency is beneficial for the NTM stabilization and the ECCD power threshold reduction. ECCD efficiency has been investigated on the J-TEXT tokamak. The electron cyclotron wave (ECW) power scan was performed to obtain the current drive efficiency. The current drive efficiency is derived to be approximately η 0 = (0.06–0.16) × 1019 A m−2 W−1 on the J-TEXT tokamak. The effect of the residual toroidal electric field has been included in the determination of the current drive efficiency, which will enhance the ECCD efficiency. At the plasma current of I p = 100 kA and electron density of n e = 1.5 × 1019 m−3, the ratio of Spitzer conductivity between omhic (OH) and ECCD phases is considered and the experimental data have been corrected. The correction results show that the current drive efficiency η 1 caused by the fast electron hot conductivity decreases by approximately 79%. It can be estimated that the driven current is approximately 24 kA at 300 kW ECW power.

Toroidal modeling of energetic passing particle drift kinetic effects on tearing mode stability

Drift kinetic effects of the neutral beam injection induced passing energetic particles (EPs) on the linear stability of the n = 1 tearing mode (TM) (with the dominant poloidal harmonic of m = 2) are numerically investigated utilizing the MARS-K code (Liu et al 2008 Phys. Plasmas 15 112503), in a tokamak plasma with finite equilibrium pressure and anisotropic thermal transport. In the low plasma pressure regime, it is found that co- (counter-) passing EPs stabilize (destabilize) the TM, agreeing with previous studies. However, as the plasma pressure increases beyond a critical value, it is found that co-passing EPs also destabilize the mode. An in-depth analysis reveals that the net effect of co-passing EPs is a result of competition between the stabilizing contribution from the non-adiabatic drift kinetic terms and the destabilizing contribution associated with adiabatic terms, with the latter becoming more dominant at higher equilibrium pressure. Non-perturbative magnetohydrodynamic-kinetic hybrid modeling also finds that co- and counter-passing EPs modify the TM eigenfunction differently, with the counter-passing EPs enhancing the sideband harmonics. Furthermore, effects of the plasma resistivity and toroidal rotation, as well as that of the equilibrium distribution of EPs in the particle pitch angle space, are also investigated, showing asymmetric results on the TM stability between the co- and counter-passing EPs. The first order finite orbit width correction is found to be stabilizing with co-passing EPs and destabilizing with counter-passing particles. Finally, drift resonances between passing EPs and the TM induce finite frequency to the mode and generate finite net torques inside the plasma, due to the neoclassical toroidal viscosity and the Reynolds stress associated with 3D perturbations.

Effect of poloidal equilibrium flow and pressure gradient on the m/n = 2/1 tearing mode

The effect of equilibrium poloidal flow and pressure gradient on the m/n = 2/1 (m is the poloidal mode number and n is the toroidal mode number) tearing mode instability for tokamak plasmas is investigated. Based on the condition of p ≠ 0 (p is plasma pressure), the radial part of the motion equation is derived and approximately solved for large poloidal mode numbers (m). By solving partial differential equations (Whittaker equation) containing second order singularity, the tearing mode stability index Δ′ is obtained. It is shown that the effect of equilibrium poloidal flow and pressure gradient has an adverse effect on the tearing mode instability when the pressure gradient is nonzero. The poloidal equilibrium flow with pressure perturbation partially reduces the stability of the classical tearing mode. But the larger pressure gradient in a certain poloidal flow velocity range can abate the adverse influence of equilibrium poloidal flow and pressure gradient. The numerical results do also indicate that the derivative of pressure gradient has a significant influence on the determination of the instability region of the poloidal flow with pressure perturbation.

Effect of fast electron transport on neoclassical tearing mode stabilization by electron cyclotron current drive

Recent studies have shown that the stabilization of neoclassical tearing modes (NTMs) by electron cyclotron current drive (ECCD) in ITER may be impeded when the injected electron cyclotron wave beam is broadened by plasma density fluctuations. This paper starts with the analysis of NTM stabilization by ECCD using the modified Rutherford equation (MRE). It is shown that with a wide wave deposition, the most effective approach for mode stabilization is to apply modulated ECCD early during the mode growth when the magnetic island is small, as expected. Numerical simulations based on reduced magnetohydrodynamic equations have been further carried out, and the results show the same trend as those obtained from the MRE. However, the perpendicular transport of fast electrons, taken into account in numerical simulations, is found to significantly degrade the mode stabilization by modulated ECCD. The modulated driven current required for mode stabilization is proportional to the square root of the perpendicular diffusivity of fast electrons and is increased by several times when the diffusivity reaches the anomalous transport level due to plasma turbulence. If the radial misalignment of the driven current from the resonant surface reaches ∼4% of the plasma minor radius, the mode stabilization can be degraded to a great extent, depending on the wave deposition width and the perpendicular diffusivity of fast electrons.

Application of Galerkin spectral method for tearing mode instability

Magnetic reconnection and tearing mode instability play a critical role in many physical processes. The application of Galerkin spectral method for tearing mode instability in two-dimensional geometry is investigated in this paper. A resistive magnetohydrodynamic code is developed, by the Galerkin spectral method both in the periodic and aperiodic directions. Spectral schemes are provided for global modes and local modes. Mode structures, resistivity scaling, convergence and stability of tearing modes are discussed. The effectiveness of the code is demonstrated, and the computational results are compared with the results using Galerkin spectral method only in the periodic direction. The numerical results show that the code using Galerkin spectral method individually allows larger time step in global and local modes simulations, and has better convergence in global modes simulations.

Overview of the FTU results

Since the 2018 IAEA FEC Conference, FTU operations have been devoted to several experiments covering a large range of topics, from the investigation of the behaviour of a liquid tin limiter to the runaway electrons mitigation and control and to the stabilization of tearing modes by electron cyclotron heating and by pellet injection. Other experiments have involved the spectroscopy of heavy metal ions, the electron density peaking in helium doped plasmas, the electron cyclotron assisted start-up and the electron temperature measurements in high temperature plasmas. The effectiveness of the laser induced breakdown spectroscopy system has been demonstrated and the new capabilities of the runaway electron imaging spectrometry system for in-flight runaways studies have been explored. Finally, a high resolution saddle coil array for MHD analysis and UV and SXR diamond detectors have been successfully tested on different plasma scenarios.